# Effect of smaller sample size on confidence intervals

Assume we were to collect 20 data samples for the passage time of light and in those 20 samples, there were 3 negative values. If we were to discard these negative values, what effect would that have when constructing confidence intervals for the mean and variation?

I know that a smaller sample size results in a larger confidence interval but what if the data is flat out incorrect (i.e. negative times such as in this example)?

A smaller sample size results in a larger confidence interval if the data are from the same distribution.

Your case is quite different. You could, of course, just take two CIs and see what happens, but, in general deleting points at one end will make the CI smaller, regardless of whether those points re wrong or not or negative or not. e.g.:

library(plotrix)
set.seed(1929191)
x <- rnorm(20)

std.error(x)

xsort <- sort(x)
xtrunc <- xsort[1:17]

std.error(xtrunc)


However, this is only true in general. Michael Mayer raises the point of right skewed distributions and deleting the smallest values, e.g.

set.seed(1929191)
x2 <- rexp(20, 2)
std.error(x2) #0.13

x2sort <- sort(x2)
x2trunc <- x2sort[3:20]

std.error(x2trunc) #0.12


and I am sure more extreme shrinkages of se.mean could occur.

• Even if the standard deviation of the observations decreases, the standard error of the estimator might increase due to the smaller sampe size. E.g. if you drop the smallest value of a right skewed distribution and consider a c.i. for the mean.. – Michael M Nov 10 '13 at 13:29